Temporal-based network embedding and prediction

ABSTRACT

Deriving network embeddings that represent attributes of, and relationships between, different nodes in a network while preserving network data temporal and structural properties is described. A network representation system generates a plurality of graph time-series representations of network data that each includes a subset of nodes and edges included in a time segment of the network data, constrained either by time or a number of edges included in the representation. A temporal graph of the network data is generated by implementing a temporal model that incorporates temporal dependencies into the graph time-series representations. From the temporal graph, network embeddings for the network data are derived, where the network embeddings capture temporal dependencies between nodes, as indicated by connecting edges, as well as temporal structural properties of the network data. Network embeddings represent network data in a low-dimensional latent space, which is useable to generate a prediction regarding the network data.

Computer-implemented networks (e.g., the Internet, social networkingplatforms, academic citation and collaboration platforms, and so forth)are increasingly used to record interactions between entities (e.g.,different computing devices connected via the network). In a graphicalrepresentation of the network, entities are represented as “nodes,” andare connected to one another via “edges.” For instance, an example graphrepresentation of different computing device nodes would create an edgebetween two nodes representing an email sent from one of the computingdevice nodes to another. Because nodes and edges continuously changeover time, it remains a challenge to derive an accurate representation,or “embedding,” that accounts for temporal dynamics and temporalstructural properties of changing nodes and edges.

Network node embeddings are often used for various downstream machinelearning objectives such as entity resolution tasks, forecasting tasks,and so forth. Accordingly, properly accounting for the temporal dynamicsand temporal structural properties is critical to the accuracy of suchdownstream machine learning objectives. Conventional approaches toderiving such network embeddings, however, are unable to properly modeltemporal dynamics and structural properties that reflect real-timechanges to such computer-implemented networks. Accordingly, conventionalsystems rely on static network embeddings that fail to account forchanging temporal network dynamics and consequently misrepresent thenetwork structure for use in downstream tasks.

SUMMARY

A system and techniques are described for deriving network embeddingsfor network data that represent attributes of, and relationshipsbetween, different nodes in a network while preserving temporaldependencies and temporal structural properties of the network data. Anetwork representation system generates a plurality of graph time-seriesrepresentations of network data that each includes a subset of nodes andedges included in a time segment of the network data. Individual graphtime-series representations are constrained either by an amount of timerepresented by, or an amount of edges included in, the graph time-seriesrepresentation, such that different graph time-series representationsgenerated from network data encompass a same amount of time or include asame amount of edges. Given the time-constrained or edge-constrainedgraph time-series representations of the network data, a temporal graphof the network data is generated by implementing a temporal model thatincorporates temporal dependencies into the graph time-seriesrepresentations.

From the temporal graph, network embeddings for the network data arederived, where the network embeddings capture temporal dependenciesbetween nodes, as indicated by connecting edges, as well as temporalstructural properties of the network data (e.g., amounts and attributesof nodes and edges). In implementations where the network data isreceived as a constant stream, the techniques described hereinconstantly derive and update network embedding based on newly receivednetwork data. The network embeddings represent network data in alow-dimensional latent space, which is useable by prediction models,classification models, and the like to generate a prediction for, orotherwise classify network data in a manner that would be intractable ifperformed on the raw network data.

This Summary introduces a selection of concepts in a simplified formthat are further described below in the Detailed Description. As such,this Summary is not intended to identify essential features of theclaimed subject matter, nor is it intended to be used as an aid indetermining the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description is described with reference to the accompanyingfigures.

FIG. 1 is an illustration of an environment in an example implementationthat is operable to employ the temporal-based network embedding andprediction techniques described herein.

FIG. 2 illustrates an example implementation in which the networkrepresentation system of FIG. 1 generates network embeddings for networkdata using techniques described herein.

FIG. 3 illustrates example implementations of graph time-seriesrepresentations of network data generated by the network representationsystem of FIG. 1 .

FIG. 4 illustrates an example implementation of temporal reachabilitygraph generated by the network representation system of FIG. 1 .

FIG. 5 illustrates an example implementation in which the predictionsystem of FIG. 1 generates a prediction using network embeddings fornetwork data using techniques described herein.

FIG. 6 is a flow diagram depicting a procedure in an exampleimplementation for deriving network embeddings from network data andgenerating a prediction based on the network embeddings using techniquesdescribed herein.

FIG. 7 is a flow diagram depicting a procedure in an exampleimplementation for generating a temporal reachability graph representingnetwork data using techniques described herein.

FIG. 8 illustrates an example system including various components of anexample device that can be implemented as a computing device asdescribed and/or utilized with reference to FIGS. 1-7 to implementtechniques described herein.

DETAILED DESCRIPTION

Overview

Networks such as social networking platforms, office intranets, theWorld Wide Web, and so forth provide a universal mechanism fororganizing diverse real-world information. Networks can be graphicallyrepresented as a series of nodes and edges, where nodes arerepresentative of network entities and edges are representative ofconnections between different network entities. Individual nodes areassociated with node attributes, which characterize real-world aspectsof the corresponding network entity. Given the vast amount of dataincluded in a single network, node/edge structural representations of anetwork are often incomplete, lacking sufficient node attributes toaccurately characterize a network entity. Given this sparse informationincluded the graphical representation of a network, various conventionalapproaches have been developed to predict missing attributes thatcharacterize nodes and/or edges of the network structure. For instance,in the context of a social networking platform, conventional approacheshave been designed to predict which communities in which a given userprofile node is a member.

Because some real-world networks include billions of nodes and edges andrepresent heterogeneous types of nodes and edges, accurately derivingpredictions from data representing an entire network is intractable. Toaddress this intractability, conventional approaches to network modelinghave been developed to learn network embeddings for a given network.Generally, these conventional approaches seek to identify a mappingfunction that converts each node in the network to a latent spacerepresentation, thus reducing a dimensionality of data representing thenetwork. From the network embeddings, conventional classification modelsare implemented to predict missing network node attributes.

Conventional approaches to deriving network embeddings break down thegraphical representation of a network into snapshots that include onlynodes and edges observed in the network over a specified duration. Suchsnapshots are created to span an application-specific duration. Forinstance, a conventional approach designed to predict node attributesover a future hour generates a snapshot that represents a previous hourof network nodes and edges. From the single snapshot graph, networkembeddings are derived and used to make predictions pertaining to thefuture hour. However, such conventional snapshot graphs fail to providean accurate representation of most network structures, given the highlydynamic nature of nodes and edges changing over time.

To address this shortcoming, other conventional approaches generatemultiple snapshot graphs (e.g., five snapshot graphs each covering oneof a previous five hours), derive network embeddings from eachindividual snapshot, and merge the network embeddings using operationstailored specifically for the predictive modeling task for which thenetwork embeddings were derived. However, these conventional approachesare restricted to the specific predictive task for which they aredesigned. Further, the operations tailed specifically for the predictivemodeling task are computationally intensive, requiring substantialamounts of computational and networking resources to complete. Forinstance, conventional network representation and embedding systems aimto merge embeddings learned from different time-constrained networksnapshots. In doing so, conventional systems introduce additional latentvariables, which are computationally expensive (e.g., requireconsiderable computational resources and time) to process and generatemerged embeddings from the different time-constrained snapshots. Thus,conventional approaches to generating network embeddings mischaracterizenetwork data and are computationally expensive to perform, consequentlyresulting in excessive consumption of computing and network resources aswell as inaccurate predictions generated from conventional networkembeddings.

Accordingly, techniques for deriving network embeddings that preservetemporal relationships and dependences in real-time streaming networkdata, and generating predictions from the network embeddings, aredescribed. A network representation system receives at least one timesegment of network data, where the time segment includes nodes and edgesthat collectively represent network activity during the time segment.From the time segment, the network representation system generates atleast one graph time-series representation of the nodes and edgesincluded in the time segment. Each graph time-series representation isconstrained to include all nodes and edges observed during a subsetduration of the time segment of network data.

Alternatively, each graph time-series representation is constrained toinclude a fixed number of edges, such that a plurality of graphtime-series representations are generated for the time segment ofnetwork data, where each graph time-series representation includes asame number of edges. Fixing a number of edges represented in a graphtime-series representation of network data advantageously enables thenetwork representation system to control structural properties of thegraph time-series representation otherwise not enabled bytime-constrained graph time-series representations. For instance, inreal-world networks, the amount of edges that occur during a given timesegment (e.g., hour, day, month, etc.) differs significantly from theamount of edges that occur during another time segment of the sameduration. In edge-constrained graph time-series representations, becausethe number of represented edges remains constant over the plurality ofgraph time-series representations generated for a time segment ofnetwork data, network embeddings learned from edge-constrained graphtime-series representations are relatively similar due to being learnedfrom a constant number of edges. For instance, given a first arbitrarygraph and a second arbitrary graph, where a number of edges in the firstarbitrary graph is much less than a number of edges in the secondarbitrary graph, the amount of network embeddings in n-node networkmotifs, or graphlets, for the second arbitrary graph is consequentlylarger than the amount of network embeddings in graphlets for the firstarbitrary graph. Consequently, by constraining graph time-seriesrepresentations by an amount of included edges, and nodes linked bythose included edges, embeddings learned from adjacent edge-constrainedgraph time-series representations are reflective of structural changesof the graph over time.

In contrast to the edge-constrained graph time-series representationsdescribed herein, conventional approaches that leverage onlytime-constrained graph time-series representations introduce uncertaintyregarding whether a difference in network embeddings learned betweenadjacent graph time-series representations stems from different numbersof edges represented in the different graph time-series representationsor whether the difference in embeddings actually represents changes innetwork structure over time.

Given the time-constrained or edge-constrained graph time-seriesrepresentations of the network data, the network representation systemgenerates a temporal graph of the network data by implementing atemporal model that incorporates temporal dependencies into the graphtime-series representations. By incorporating temporal dependencies intothe graph time-series representations, the network representation systemadvantageously preserves temporal constraints otherwise disregarded byconventional approaches, such as the snapshot graph approach thatdiscards temporal relationships occurring across multiple snapshotgraphs for the same network data. By incorporating temporal dependenciesinto the graph time-series representations, the network representationsystem is configured to learn time-dependent network embeddings for thenodes and edges included in the network data.

In some implementations, the temporal dependency of the network data isrepresented as a temporal reachability graph, which represents a novelgraphical structure not contemplated by conventional network modelingapproaches. In generating the temporal reachability graph, the networkrepresentation system identifies one or more node pairs included in thenetwork data that are not directly connected by one of the edges, butare temporally connected via a sequence of multiple edges within aspecified time interval. In response to identifying that the node pairis temporally connected, an edge directly linking the node pair is addedto the temporal reachability graph. The temporal reachability graphfurther acknowledges temporal properties with respect to added edges, byconstraining the sequence of edges to follow a directionality of timeduring the specified interval. In this manner, a sequence of edges thatotherwise connect a node pair during the specified interval but are nottemporally ordered in a manner that follows time is not used as a basisto add an edge directly connecting the node pair in the temporalreachability graph.

In some implementations, the network representation system is furtherconfigured to generate a weighted version of the temporal reachabilitygraph, where weights are assigned to the additional edges indicating atemporal strength of reachability (e.g., a time required to complete thesequence of edges serving as the basis for generating the additionaledge, a number of temporally valid paths connecting the node pair, orcombinations thereof). By adding and optionally weighting such edges, atemporal reachability graph for network data represents a feasible datatransmission path or connection between two nodes, thus providingadditional contextual information regarding network structure and noderelationships not otherwise explicitly set forth in the network data. Assuch, the temporal reachability graph derived using techniques describedherein provides additional network information otherwise not consideredby conventional network modeling approaches, which results in networkembeddings having increased accuracy.

Given the temporal graph generated from the graph time-seriesrepresentations of the network data, the network representation systemis configured to derive network embeddings from the temporal graph byemploying one or more embedding methods. The network embeddings capturetemporal dependencies between nodes, as indicated by connecting edges,as well as temporal structural properties of the network data (e.g.,amounts and attributes of nodes and edges). Advantageously, thetechniques described herein enable continuously deriving and updatingnetwork embeddings for a constant stream of network data, which capturesand preserves temporal relationships that are unable to be maintained byconventional network modeling approaches. The particular embeddingmethod implemented to generate the network embeddings depends on aparticular predictive task or objective for which the network embeddingsare to be leveraged.

Given the network embeddings, a prediction system is employed togenerate a prediction for the network data. Example predictionsgenerated from the network embeddings derived using techniques describedherein include a link prediction that indicates a missing edge in thenetwork data that is likely to occur in the future or is likely to havepreviously occurred but is not represented in the network data. Anotherexample prediction includes a node attribute prediction, which indicatesa node attribute value that is not included in the received networkdata. The network embeddings derived using techniques described herein,however, are not so limited to these example predictive tasks orobjectives, and are configured to be leveraged by any predictive,classification, and other model types configured to generate outputsfrom latent space representations of network data. Because the graphtime-series representations and temporal graphs generated from networkdata are agnostic with respect to a downstream predictive task, thetechniques described herein advantageously require fewer computationaland network resources relative to conventional approaches that requirelearnable parameters and performance of specific operations, bothtailored for a particular predictive task. Due to the preservation oftemporal dependencies and temporal structural changes of network data,as well as the decreased computational resources required relative toconventional approaches, the techniques described herein generatenetwork embeddings in an efficient manner that are useable to generatemore reliable network predictions than conventional systems.

Example Environment

FIG. 1 is an illustration of a digital medium environment 100 in anexample implementation that is operable to employ the techniquesdescribed herein. The illustrated environment 100 includes a computingdevice 102, which is implementable according to a variety ofconfigurations. For instance, the computing device 102 is configurableas a desktop computer, a laptop computer, a mobile device (e.g.,assuming a handheld configuration such as a tablet or mobile phone), andso forth. Thus, the computing device 102 is representative of a fullresource device having substantial memory and processor resources (e.g.,a personal computer, a server computing device, and the like) as well asa low-resource device having comparatively limited memory and/orprocessing resources (e.g., a mobile device). In some implementations,although only a single computing device 102 is illustrated in FIG. 1 ,the computing device 102 is representative of a plurality of differentdevices, such as multiple server computing devices that are configuredto collaboratively perform operations via “the cloud,” as described infurther detail below with respect to FIG. 8 .

The computing device 102 includes a network representation system 104and a prediction system 106. The network representation system 104represents functionality of a computing device to generate alow-dimensional latent representation of data obtained via one or morenetworks, collectively represented by network data 108 in theillustrated environment 100. The low-dimensional latent representationof the network data 108 is represented by the network embeddings 110output by the network representation system 104. As described herein,the low-dimensional latent representation of the network data 108included in the network embeddings 110 provides a metric for evaluatingsimilarities and differences between entities represented in the networkdata 108.

For instance, in an implementation where the network embeddings 110comprise a two-dimensional latent representation of the network data108, a distance between two entities represented in the networkembeddings 110 indicates a similarity between one or more attributes ofthe two entities (e.g., closer distance indicates greater similarityrelative to further distance). In this manner, the network embeddings110 represent one or more mapping functions that define the latentrepresentation for each entity represented in the network data 108 aswell as the latent representation for each connection between two ormore entities represented in the network data 108.

As described in further detail below, the network embeddings 110generated by the network representation system 104 according to thetechniques described herein are configured to be leveraged by a range ofdifferent network classification models and/or network prediction modelstrained to generate a prediction from low-dimensional latentrepresentations of network data. Given the network embeddings 110, theprediction module 106 is configured to generate a prediction 112corresponding to the network data 108. The network data 108 isrepresentative of information describing different entities and observedconnections between the different entities during a time segment 114.

Each of the entities (e.g., a computing device, a physical location, auser profile, an Internet Protocol (IP) address, a Uniform ResourceIdentifier (URI) for a resource accessible via a network represented bythe network data 108, a user profile, or an institution identifying aplurality of user profiles) are represented as a node 116 in the networkdata 108. Connections between the entities (e.g., a transmission of datafrom one computing device node to another computing device node, anaccess of a URI by an IP address, a computing device associating with anIP address, a correlation of an IP address to a physical location,satisfaction of a threshold physical distance between two computingdevices, and so forth) are represented as edges 118 in the network data108.

In this manner, the network data 108 includes data useable to generate agraphical representation of the nodes 116 and edges 118 during the timesegment 114, where each node 116 represents an entity observed by anetwork during the time segment 114 and each edge 118 represents aconnection between two different nodes 116 during the time segment 114.Each edge 118 included in the network data 108 includes informationspecifying a source node 116 and a destination node 116 connected by theedge 118 as well as information denoting a time at which the edge 118occurred during the time segment 114.

In accordance with one or more implementations, nodes 116 are receivedas part of network data 108 with corresponding information describing atleast one attribute for the node. For instance, in an example scenariowhere a node 116 represents a computing device, the network data 108includes information describing attributes of the computing device, suchas a device type, a serial number, a version of software implemented bythe computing device, and so forth. As another example, for a node 116representing a user profile, the network data 108 may includeinformation describing node attributes such as a name or otheridentifier of an individual associated with the user profile, an age ofthe individual, a geographic location associated with the user profile,a gender of the individual associated with the user profile, aneducational or workplace institution associated with the user profile,and so forth.

In this manner, specific entities, information, and connectionsrepresented by each of the nodes 116 and edges 118 of the network data108 is constrained only by a source network from which the network data108 was received. For instance, network data 108 received from a socialnetworking platform predominantly comprising nodes 116 representing userprofiles and edges 118 representing likes, comments, shares, and soforth between different user profiles differs from network data 108received from a mobile service provider platform where nodes 116represent different computing devices and physical locations and edges118 represent calls, messages, and the like between different computingdevices as well as physical proximities of the different computingdevices to the physical locations. Using the techniques describedherein, the network representation system 104 is configured toaccommodate such disparate network data 108 and generate networkembeddings 110 that map the noes 116 and edges 118 to a common latentspace.

The prediction 112 generated by the prediction system 106 from thenetwork embeddings 110 depends on a particular prediction orclassification model implemented by the prediction system 106. Theprediction 112 specifies one or more of a transmission path 120 or anode attribute 122 for the network data 108. The transmission path 120is representative of one or more edges 118 that are predicted to occurin the future (e.g., one or more edges 118 not included in the networkdata 108). The node attribute 122 is representative of an estimatedattribute for one of the nodes 116 in the network data 108, where thenode attribute 122 represents information that was not included in thenetwork data 108 describing one of the nodes 116.

To generate the network embeddings 110, the network representationsystem 104 employs a graph time-series module 124, a temporal modelingmodule 126, an embedding module 128, and a time-series summarization(T-SS) module 130. The graph-time series module 124, the temporalmodeling module 126, the embedding module 128, and the T-SS module 130are each implemented at least partially in hardware of the computingdevice 102 (e.g., through use of a processing system andcomputer-readable storage media), as described in further detail belowwith respect to FIG. 8 .

The graph time-series module 124 is configured to generate one or moregraph time-series representations of the network data 108. As describedin further detail below with respect to FIGS. 2 and 3 , the graphtime-series representation(s) generated by the graph time-series module124 are constrained to encompass one of a fixed duration of time (e.g.,a portion or entirety of the time segment 114) or a fixed number ofedges (e.g., a designated subset number of the edges 118 included in thenetwork data 108). When generating a graph time-series representationconstrained by a time interval, the graph time-series representationincludes all edges 118 included in the network data that were observedduring the time interval. Conversely, when generating a graphtime-series representation constrained by a number of edges, the graphtime-series representation includes the fixed number of edges withoutbeing restricted to encompass a certain duration of the time segment114.

In certain implementations, by generating graph time-seriesrepresentations of the network data constrained by a number of edgesincluded in the graph time-series representation, the graph time-seriesmodule 124 reduces ambiguities in the resulting network embeddings 110resulting from structural changes in the network data 108 over time thatotherwise exist when generating the resulting network embeddings 110from graph time-series representations constrained by time.

The temporal modeling module 126 is configured to generate, from thegraph time-series representation(s), a temporal graph of the networkdata. To do so, the temporal modeling module 126 is configured toimplement a model that incorporates temporal dependencies into thegraph-time series representation(s) to learn time-dependent embeddingsfor nodes 116 and/or edges 118 included in the network data. In someimplementations, the temporal modeling module 126 generates a temporalreachability graph for the network data 108. The temporal reachabilitygraph representing the network data 108 includes at least one edge thatdirectly links two of the nodes 116 that were not directly linked viaone of the edges 118 included in the network data. By adding such anedge, the temporal reachability graph for the network data 108represents a feasible transmission path between two of the nodes 116during a specified time interval, thereby providing additionalcontextual information regarding relationships between the nodes 116 notexplicitly set forth in the network data 108. Additional detailsregarding generation of a temporal reachability graph and other exampletemporal graphs generated by the temporal modeling module are describedin further detail below with respect to FIGS. 2 and 4 .

The embedding module 128 is configured to derive a time-series ofnetwork embeddings from the temporal graph generated by the temporalmodeling module 126. To do so, the embedding module 128 employs anembedding model that is dependent on a task or objective for which thetime-series of network embeddings are to be used (e.g., a type ofprediction to be generated for the network data 108). For instance, theembedding module 128 is configured to employ a community/proximity-basedembedding model, a role-based embedding model, a hybrid embedding modelbased on structural similarity of node-central subgraphs, combinationsthereof, and so forth. Notably, the embedding module 128 is configuredto employ any type of existing static embedding method, as the temporalgraph 214 generated using the techniques described herein is bothgeneric and expressive to degrees that enable derivation of networkembeddings by static embedding methods. The time-series of networkembeddings output by the embedding module 128 are representative of anexample instance of the network embeddings 110.

The T-SS module 130 is configured to further process the time-series ofnetwork embeddings output by the embedding model 128 to improve apredictive performance of the prediction system 106. For instance, in anexample scenario where the network data 108 is received by the computingdevice 102 as a continuous stream of time segments 114, the graphtime-series module 124 is configured to generate a plurality of graphtime-series representations that represent segments of the continuousstream. The temporal modeling module 126 is configured to generate atemporal graph for each of the plurality of graph time-seriesrepresentations, which in turn are used by the embedding module 128 togenerate a plurality of time-series of network embeddings. The T-SSmodule 130 is configured to temporally weight embeddings byconcatenating or aggregating the plurality of time-series of networkembeddings for use in temporal prediction tasks. The T-SS module's 130processing of the time-series of network embeddings generated by theembedding module 128 is optional, and thus both the time-series ofnetwork embeddings generated by the embedding module 128 as well as theaggregated or concatenated network embeddings output by the TS-S module130 are examples of the network embeddings 110 generated by the networkrepresentation system 104.

To generate the prediction 112 from the network embeddings 110, theprediction system 106 employs a prediction module 132. The predictionmodule 132 is configured to implement a prediction model configured fora particular task or objective and cause the prediction model togenerate prediction 112 by providing the network embeddings 110 as inputto the prediction model. For instance, to generate the transmission path120 prediction, the prediction module 132 is configured to implement alink prediction model that outputs predictions of future edges 118between nodes 116 when provided the network embeddings 110 as input. Inanother example, to generate the node attribute 122 prediction, theprediction module 132 is configured to implement an entity attributeprediction model that outputs predictions of at least one attributevalue for one or more of the nodes 116 when provided the networkembeddings 110 as input.

Accordingly, the prediction system 106 is configured to implement thenetwork embeddings 110 generated by the network representation system104 to output predictions that indicate at least one of a missingattribute value not included in the network data 108 or a future edge118 between nodes 116 of the network. In this manner, the techniquesdescribed herein enable generating a prediction by leveraging networkdata 108 obtained from a particular network data source 134 (e.g., asocial networking platform, a mobile service provider, a web server,etc.) or from a plurality of different network data sources 134,collectively represented as network 136.

Having considered an example digital medium environment, consider now adiscussion of an example system useable to generate network embeddings110 and generate a prediction 112 in accordance with aspects of thedisclosure herein.

FIG. 2 illustrates an example system 200 useable to generate networkembeddings 110 for network data 108 using the techniques describedherein. In the illustrated example, system 200 includes modules of thenetwork representation system 104 as described with respect to FIG. 1 ,e.g., the graph time-series module 124, the temporal modeling module126, the embedding module 128, and the T-SS module 130. System 200 isconfigured to be implemented on a single computing device (e.g.,computing device 102 of FIG. 1 ) or a combination of multiple computingdevices, as described in further detail below with respect to FIG. 8 .

In the example system 200, the graph time-series module 124 isconfigured to receive at least one time segment 114 of network data 108,where the time segment 114 includes information describing nodes 116 andedges 118 observed by one or more networks during a time periodconstrained by the time segment 114. In some implementations, thenetwork data 108 is received as a temporal graph, which is a graphicalrepresentation of the nodes 116 and edges 118. In the temporal graph,timestamps of the edges 118 are represented as specific time values thatdescribe a temporal occurrence of the edge 118 connecting two of thenodes 116. In the temporal graph, nodes 116 are represented as V. Theedges 118, E, between nodes 116 are represented as E⊆V×V×

⁺. Each edge 118 is represented as (u,v,t), where u and v representnodes 116 connected by the edge, and t denotes a time at which theconnection occurred, where t∈

⁺. The time segment 114 of the network data 108 is thus represented byG=(V,E).

The graph time-series module 124 is configured to analyze the networkdata 108 to identify one or more temporal walks within the temporalgraph representation of the network data 108. In a temporal graph, atemporal walk describes a transmission path among nodes 116 of the graphthat is constrained by time. For instance, in an example scenario wherean edge 118 between nodes u and w represents a transfer of data betweentwo entities, a temporal walk represents a feasible route fortransferring that data. In this manner, a temporal walk from node u tovertex w in the temporal graph G is a sequence of edges e₁, . . . e_(k),such that e₁=(u₁,u₂,t₁), . . . , e_(k)=(u_(k),u_(k+1),t_(k)) wheret_(j)<t_(j+1) for all j=1 to k.

If a temporal walk exists between nodes 116, the nodes 116 aretemporally connected. By constraining paths between nodes with respectto time, temporal walks are constrained to follow the directionality oftime. In order to generate the network embeddings 110 from the networkdata 108, the graph time-series module 124 is configured to generate atleast one graph time-series representation 202 of the nodes 116 andedges 118 included in the time segment 114. The graph time-series module124 is configured to generate the graph time-series representation 202as either a τ-graph time-series representation 204 or an ϵ-graphtime-series representation 206.

Given time segment 114 of the network data 108, G=(V,E), where E isrepresentative of a continuous stream of timestamped edges 118 e₁, e₂,e₃, . . . , e_(t−1), e_(t), . . . , a τ-graph time-series representation204 of the temporal graph is defined as G^(T)={G₁, . . . , G_(k), . . ., G_(t)}. In the τ-graph time-series representation 204 of G, G₁consists of all edges 118 within a first time scale, or period, denoted“s,” G₂ consists of all edges within a second time period s, and soforth. The time scale represented by the τ-graph time-seriesrepresentation 204 is configured to encompass all or a portion of theduration encompassed by time segment 114. In this manner, if t₀ denotesthe timestamp of the first edge 118 in the stream of timestamped edgesrepresented by the temporal graph G, where τ represents the period ortime-scale represented by G (e.g., one hour, one day, one month, etc.),then the edges E_(k) represented in G_(k) are defined according toEquation 1:E _(k)={(i,j,t)∈E|t ₀ +kτ>t≥t ₀+(k−1)τ}  (Eq. 1)

Consequently, the τ-graph time-series representation 204 corresponds toa time-series of graphs representing a stream of timestamped edges,where each of the time-series of graphs spans a common duration (e.g., asame time-scale or period) and the stream of timestamped edgesrepresented in each of the time-series of graphs includes those edgeshaving associated timestamps that occur during the duration bounded bythe graph time-series representation 202. In this manner, whenconfigured as a τ-graph time-series representation 204, an amount ofedges included in G₁ are configured to differ with respect to an amountof edges included in G₂, and so forth.

In contrast to a τ-graph time-series representation 204, whichrepresents all edges observed over a specified duration of time (e.g., asegment of the time segment 114), an ϵ-graph time-series representation204 refers to a representation of G=(V,E) defined as G^(ϵ)={G₁, . . . ,G_(k), . . . , G_(t)}, where each G_(k) includes a fixed number of theedges 118 (e.g., ϵ edges). In this manner, |E_(k)|=∈, ∀k. Stateddifferently, ϵ denotes a fixed number of temporal edges in thetime-ordered stream of edges represented by E, |E_(k)|=∈ for all k=1, 2,. . . , and so forth. As such, G₁=(E,V) consists of the first ∈ edges118 E₁={e₁, e₂, . . . , e_(∈)). Extrapolating, G₂ consists of the next ∈edges 118 E₂={e_(ε+1), e_(∈+2), e_(2∈)), and so forth. Accordingly,E_(t) is defined according to Equation 2 for an ϵ-graph time-seriesrepresentation 206.

$\begin{matrix}{E_{t} = {{\overset{t\;\epsilon}{\bigcup\limits_{i = {{{({t - 1})}\epsilon} + 1}}}e_{i}} = \left\{ {e_{{{({t - 1})}\epsilon} + 1},\ldots\mspace{14mu},\epsilon_{t\;\epsilon}} \right\}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$

By modeling G=(V,E) using the ϵ-graph time-series representation 206,each graph time-series G_(k) includes a common, fixed number of edges.Fixing a number of edges 118 represented using the ϵ-graph time-seriesrepresentation 206 advantageously enables the graph-time series module124 to control structural properties otherwise not enabled by theτ-graph time-series representation 204. For instance, because a numberof represented edges 118 remain constant over different ϵ-graphtime-series representations 206, embeddings learned from E_(t) arerelatively similar, due to being learned from the same number of edges118. In contrast, the τ-graph time-series representation 204 introducesuncertainty regarding whether a difference in embeddings betweenadjacent time-series (e.g., from t to t+1) is due to the number of edges118 represented in different τ-graph time-series representations 204 fort and t+1, or whether the difference in embeddings is due to changes innetwork structure over time (e.g., due to changes in a number of nodes116 observed during the durations encompassed by t and t+1.

FIG. 3 illustrates an example implementation 300 of an example graphicalrepresentation of network data 108 along with an example τ-graphtime-series representation 204 and example ϵ-graph time-seriesrepresentation 206 derived from the network data 108. In the exampleimplementation 300, network data 302 illustrates an example graphicalrepresentation of network data 108. Network data 302 illustrates aplurality of edges 304, depicted as arrows, connecting nodes 306 and308, depicted as circles. The arrow of each edge 304 represents adirectionality of a connection between nodes 306 and 306, where node 306represents a source node and node 308 represents a destination node. Forinstance, in an example scenario where edge 304 represents a transfer ofdata (e.g., a phone call, an email, etc.) edge 304 indicates that thedata was transferred from node 306 to node 308. The network data 302 isfurther illustrated as segmented into a plurality of time intervals 310,312, 314, and 316. Each time interval 310, 312, 314, and 316 correspondsto all or a portion of the time segment 114.

Example τ-graph time-series representations 204 derived from the networkdata 302 are characterized by representations 318, 320, 322, and 324. Asevidenced by the illustrated example 300, the different τ-graphtime-series representations 318, 320, 322, and 324 each span anequivalent time duration (e.g., each of the τ-graph time-seriesrepresentations 318, 320, 322, and 324 encompass a corresponding one ofthe time intervals 310, 312, 314, and 316. As such, a τ-graphtime-series representation 204 of network data 108 is constrained by atime interval and includes information specifying all nodes 116 andedges 118 included in the network data 108 within the time interval. Inthis manner, an amount of edges included in one τ-graph time-seriesrepresentation 204 is variable with respect to amount of edges includedin another τ-graph time-series representation 204, even when the τ-graphtime-series representations 204 are derived from the same network data108. For instance, representation 318 includes four edges,representation 320 includes one edge, representation 322 includes threeedges, and so forth.

In contrast to a τ-graph time-series representation 204, an ϵ-graphtime-series representation 206 is constrained based on a number of edges118 included in the representation. For instance, example ϵ-graphtime-series representations 206 derived from the network data 302 arecharacterized by representations 326, 328, and 330. As evidenced in theillustrated example 300, the different ϵ-graph time-seriesrepresentations 326 are configured to encompass a specified number ofedges (e.g., 3 edges in the illustrated example 300) without constraintto durations of time during which the edges occurred in network data302.

For instance, ϵ-graph time-series representation 326 encompasses only aportion of the time interval 310, while ϵ-graph time-seriesrepresentation 328 encompasses an entirety of time duration 312 andportions of time durations 310 and 314. ϵ-graph time-seriesrepresentation 330 encompasses portions of time durations 314 and 316.Fixing a number of edges 118 represented using the ϵ-graph time-seriesrepresentation 206 advantageously enables the graph-time series module124 to control structural properties otherwise not enabled by theτ-graph time-series representation 204, which creates uncertaintyregarding whether resulting network embeddings 110 from temporallyadjacent τ-graph time-series representation 204 result from differentedges included in the different τ-graph time-series representations 204or from actual changes in a network structure represented by networkdata 108.

Returning to FIG. 2 , given the at least one graph time-seriesrepresentation 202 for the time segment 114, the temporal modelingmodule 126 is configured to generate a temporal graph 214 of the networkdata 108 by employing a temporal network model. The temporal networkmodel employed by the temporal modeling module 126 is a model thatincorporates temporal dependencies (e.g., temporal walk constraints)into the graph time-series representations 202 to learn time-dependentembeddings for entities represented by nodes 116. The temporal modelingmodule 126 is configured to implement any such temporal network model,such as a snapshot graph (SG) model 208, a temporal summary graph (TSG)model 210, or a temporal reachability graph (TRG) model 212. Althoughthe SG model 208, the TSG model 210, and the TRG model 212 are describedherein as examples to provide context regarding functionality of thetemporal modeling module 126, the temporal network model employed by thetemporal modeling module 126 is not restricted to these example models.

The SG model 208 leverages one of the τ-graph time-series representation204 or ϵ-graph time-series representation 206 directly, without encodingany additional temporal information into the representation. In thismanner, the existing temporal information (e.g., the timestamps)associated with the edges 118 in a graph G_(t) are effectivelydiscarded. Stated differently, the sequential connections orinteractions between nodes 116, represented by edges 118, in the graphG_(t) are ignored. Rather, the snapshot graph model incorporatestemporal dependencies at the time-series level of the graph. Forinstance, G_(t−1) is known to occur prior to G_(t). In this manner, thetemporal graph 214 generated by the SG model 208 is a snapshot graph(SG) 216, where each SG 216 represents a corresponding graph time-seriesrepresentation 202 from which it was generated. Temporal information forthe network data 108 is thus gleaned by considering a series of SGs 216.

In contrast to the SG model 208 approach, a TSG model 210 incorporatestemporal dependencies from the τ-graph time-series representation 204 orc-graph time-series representation 206 by assigning edges 118mathematical weights based on a timestamp associated with the edge 118.Specifically, the TSG model 210 assigns more recent edges 118 largermathematical weights relative to edges that occurred further in thepast. To do so, the TSG model 210 generates a time-series of adjacencymatrices A₁, A₂, A₃, . . . , A_(t), . . . , A_(T) from the τ-graphtime-series representation 204 or ϵ-graph time-series representation206, where A_(t)(i,j) denotes the (i,j) entry of A_(t). Operation of aweighted TSG model 210 is thus defined according to Equation 3.

$\begin{matrix}{S = {\sum\limits_{t = 1}^{T}{f\left( {A_{t},\alpha} \right)}}} & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$

In Equation 3, f represents a decay function configured to temporallyweight the edges represented in the graph time-series representation 202input to the TSG model 210. α represents a decay factor ranging in(0,1), T represents the total number of graphs included in the graphtime-series representation 202, and S is the weighted temporal summarygraph (TSG) 218 output by the TSG model 210. In accordance with one ormore implementations, f represents an exponential decay function, suchthat the weighted TSG 218 is represented by Equation 4.

$\begin{matrix}{S = {\sum\limits_{t = 1}^{T}{\left( {1 - \alpha} \right)^{T - t}A_{t}}}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$

Because the weight for an edge (i,j) 118 is represented asS(i,j)=E_(t=1) ^(T)(1−α)^(T−t)A_(t)(i,j) the weighted TSG S 218 isrepresented by Equation 5.S=(1−α)^(T−1) A ₁+(1−α)^(T−2) A ₂+ . . . +(1−α)A _(t−1) +A _(t)  (Eq. 5)

In this manner, the TSG model 210 is configured to leverage either theτ-graph time-series representation 204 or ϵ-graph time-seriesrepresentation 206 output by the graph time-series module 124.

In some implementations, the TSG model 210 is configured to leveragefewer than all available graphs included in the graph time-seriesrepresentation 202. For instance, the TSG model 210 is configured toleverage only the L most recent graphs represented in the graphtime-series representation 202. In one example, the TSG model 210considers only the L most recent graphs represented in the graphtime-series representation 202 when the network data 108 is received asa continuous stream of different time segments 114 and a graphtime-series representation 202 is generated for each time segment 114.

For instance, consider an example scenario where the TSG model 210receives an ϵ-graph time-series representation 206 including T graphsfrom the graph time-series module 126. In this example scenario, theϵ-graph time-series representation 206 is represented asG^(∈)={G_(t)}_(t=T) ^(T)={G₁, . . . , G_(T)}. Instead of using all Tgraphs, leveraging only the most recent L graphs is described asconsidering the graphs of G^(∈) as designated by Equation 6.G ^(∈) ={G _(t)}_(t=T−L+1) ^(T) ={G _(T−L+1) , . . . ,G _(T)}  (Eq. 6)

By leveraging only the most recent graphs, the TSG model 210 disregardsedges 118 representing connections established between nodes 116 furtherin the past (e.g., edges 118 occurring prior to edges represented in theL most recent graphs). This consideration of only the L most recentgraphs is not restricted to the TSG model 210, and in someimplementations is implemented by one or more different models employedby the temporal modeling module 214.

One example of another such model is a temporal reachability graph (TRG)model 212. The TRG model 212 is configured to derive a graph from thetimestamped edge stream as represented by the τ-graph time-seriesrepresentation 204 or ϵ-graph time-series representation 206. Notably,the TRG model 212 is configured to add a link between two nodes 116 ifthe nodes are temporally connected (e.g., if there is a temporal walkfrom one node to the other). In this manner, if the τ-graph time-seriesrepresentation 204 or ϵ-graph time-series representation 206 indicatesthe existence of a temporal walk from node u to node v, the TRG model212 generates a temporal reachability graph (TRG) 220 that includes anedge connecting node u to node v.

In this manner, for a given interval I∈

⁺ (e.g., all or a portion of time segment 114), the TRG 220 for theinterval is defined as G_(R)=(V,E_(R)), such that the TRG 220 s adirected graph where an edge (u,v)∈E_(R) in the TRG 220 denotes theexistence of a temporal walk leaving u and arriving at v during theinterval I. The number of edges included in the interval I are denotedas ω and defined by the τ-graph time-series representation 204 orϵ-graph time-series representation 206 received from the graphtime-series module 124.

In this manner, the TRG 220 generated by the TRG model 212 is a static,unweighted graph where each edge between nodes in the graph represents atemporally-valid walk beginning at the source node and reaching thedestination node. While the TRG 220 preserves temporal limitations, itfails to represent a strength of reachability, such as an amount of timerequired to complete the temporally-valid walk from a source node to adestination node.

To account for node reachability strength, or the amount of timerequired to complete temporally-valid walks from source to destinationnodes 116, the TRG model 212 is configured to generate a weighted TRG220 that represents a strength of reachability from one node to anotherby graph weights. To do so, the strength of reachability between a pairof nodes (i,j) 116 is defined as a function of both the number oftemporally-valid paths between the node pair and the timestampdifference required to complete the temporally-valid paths. Inaccordance with one or more implementations, the weighting functionimplemented by the TRG model 212 in generating the weighted temporalreachability graph is represented by Equation 7.

$\begin{matrix}{g_{i,j} = {\sum\limits_{w \in W}e^{- {({{\Delta L_{i,j}}❘w})}}}} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$

In Equation 7, w represents a specific temporally-valid walk from node ito node j, and Δt_(i,j) is representative of the temporal delay involvedin reaching j from i along that specific temporally-valid walk. In thismanner, an example implementation of deriving the weighted temporalreachability graph is performed according to the process set forth belowin Algorithm 1.

Central to the operation of Algorithm 1 is the concept of atemporally-reachable neighborhood for a given node 116. For instance,for a node i, the temporally-reachable neighborhood N_(i) ^(R) includesnodes that can be reached by i during a specified interval and recordstimestamps associated with temporal paths connecting i to other nodes.Specifically, the temporally-reachable neighborhood N_(i) ^(R) for nodei is defined as the set of tuples {(j,t_(j))}, where j represents a nodethat is reachable from i following a temporally-valid walk and t_(j)represents the timestamp of the edge reaching j from i in thattemporally-valid walk.

As noted below in Algorithm 1, given an input temporal edge (i,j,t), theset of reachable neighbors set forth in the temporally-reachableneighborhood N_(i) ^(R) are looped through to add edges in the weightedTRG 220 in the manner set forth in Equation 7, as set forth in lines 5-8of Algorithm 1. Algorithm 1 further adds (i,j) to the weighted TRG 220along with the immediate weight, as set forth in lines 9-11.

Algorithm 1 1: procedure Temporal Reachability Graph (G = (V, E)) 2: Set E_(R) = Ø 3:  Sort E_(T) in reverse time order 4:  while next edge(i, j, t) ∈ E do 5:   for (k, t_(k)) ∈ N_(j) ^(R) do 6:    E_(R) ← E_(R)∪ {(i, k)} 7:    g_(i,k) = g_(i,k) + e^(−(t) ^(k) ^(-t)) 8:    N_(i)^(R) ← N_(i) ^(R) ∪ {(k, t_(k))} 9:   E_(R) ← E_(R) ∪ {(i, j)} 10:  g_(i,j) = g_(i,j) + 1  

 Δt_(i,j) = 0 because i, j are adjacent 11:   N_(i) ^(R) ← N_(i) ^(R) ∪{(j, t)} 12:  end while 13:  return G_(R) = (V, E_(R), g)

Under Algorithm 1, the number of edges in the weighted TRG 220 (G_(R))is bounded by the number of temporally-valid walks in G. As noted above,an edge (u,v)∈E_(R) indicates a temporally-valid walk reaching from u tov in G. However, in some implementations such an example edgecorresponds to multiple unique temporal walks with differentintermediate nodes connecting u to v and/or different associatedtimestamps. Consequently, |E_(R)| must be less than or equal to thenumber of temporally-valid walks in G.

As noted above, because the TRG 220 is comprised of edges 118 within theinterval of window size ω, the edges in the temporal reachability graphinclude up to ω different temporal walks originating from a specificnode i. Consequently, the number or edges originating from a node i in aweighted temporal reachability graph is bounded by the number oftemporally-valid walks, which is also ω.

The temporal modeling module 126 is thus configured to generate twovariants of a weighted TRG 220 using the TRG model 212, one for each ofthe τ-graph time-series representation and the ϵ-graph time-seriesrepresentation generated by the graph time-series module. The temporalgraphs 214 output by the temporal modeling module 126 (e.g., the SGs216, the TSGs 218, the TRGs 220, and weighted variants thereof) derivedfrom the graph time-series representations 202 are then passed to theembedding module 128 for use in deriving network embeddings 110 for thenetwork data 108.

FIG. 4 illustrates an example implementation 400 of a TRG 220 derivedfrom a graph time-series representation 202 using the techniquesdescribed herein. In the example implementation 400, temporal graph 402represents an example instance of a time segment 114 of network data108. Nodes 404, 406, 408, 410, and 412 are representative of nodes 116and edges 414, 416, 418, and 420 are representative of edges 118. Eachof the edges 414, 416, 418, and 420 are associated with a timestamp,indicating a temporal occurrence of the edge 118 during the time segment114. For instance, edge 414 is illustrated as occurring at t₁, edge 416is illustrated as occurring at t₂, edge 418 is illustrated as occurringat t₃, and edge 420 is illustrated as occurring at t₄, wheret₁<t₂<t₃<t₄.

The temporal reachability graph 422 represents an instance of a TRG 220generated by the temporal modeling module 126 by providing the graphtime-series representation 202 as input to TRG model 212. Notably, thetemporal reachability graph 422 includes additional edges 424 and 426directly linking nodes that are not directly linked in the temporalgraph 402. Each additional edge included in the temporal reachabilitygraph 422 represents a temporally valid walk between two nodes thatoccur within a specified interval.

For instance, assuming a specified interval of t₀ to t₄ for the temporalreachability graph 422, the temporal modeling module 126 identifies thatthe sequence of edges 414 and 416 as well as the sequence of edges 414and 420 are temporally valid walks between nodes 404 and 408 and betweennodes 404 and 410, respectively. As described above, because temporalwalks between nodes are constrained to follow the directionality oftime, an edge directly connecting nodes 404 and 412 is not added to thetemporal reachability graph 422, despite the existence of a series ofedges 414, 420, and 418 there between, due to edge 420 occurringsubsequent to edge 418.

In some implementations, the temporal modeling module 126 is configuredto generate a weighted version of the temporal reachability graph 422 byassigning mathematical weights to edges added by the TRG model 212 thatwere not included in the graph time-series representation 202 (e.g.,edges 424 and 426). In some implementations, the weighted version oftemporal reachability graph 422 is weighted to indicate a temporalcloseness of added edges 424 and 426. For instance, because edge 424requires t₂−t₁ to complete and edge 426 requires t₄−t₁ to complete, edge424 is assigned a greater weight to indicate that node 408 is temporallycloser to node 404 than node 410 to node 404.

Thus, the temporal reachability graph 422, and its weighted variant,represent examples of a temporal graph 214 generated by the temporalmodeling module 126 that incorporates temporal dependencies (e.g.,temporal walk constraints) into the graph time-series representations202 to learn time-dependent embeddings for entities represented by nodes116 and connecting edges 118.

Returning to FIG. 2 , the temporal graph(s) 214 are then passed to thenode/edge embedding module for combination. The embedding module 128 isconfigured to employ an embedding method given the temporal graph 214 asinput and generate a time-series of network embeddings 222 derived fromthe temporal graph 214. The time-series of network embeddings 222captures temporal dependencies represented between nodes 116, asindicated by connecting edges 118, of the network data 108 as well astemporal structural properties of the network data 108 (e.g., amountsand attributes of nodes 116 and amounts of edges 118). The particularembedding method implemented by the embedding module 128 is dependent ona particular predictive task or objective for which the time-series ofnetwork embeddings 222 are to be employed.

For instance, in some implementations the embedding model implemented bythe embedding module 128 is a community/proximity-based embeddingmethod, a role-based embedding method, or a hybrid method based onstructural similarity of node-central subgraphs. Examples ofcommunity/proximity-based embedding methods include LINE, Node2vec, andGraph2Gaussian models. Examples of role-based embedding methods includestruc2vec, Role2vec, and Graphwave models. An example of a hybrid methodbased on structural similarity of node-central subgraphs includes theMultilens embedding model. While combining the embeddings over the graphtime-series representations represented by the temporal graphs 214 isperformed according to a specific embedding model implemented by theembedding module 128, Algorithm 2 provides a general frameworkdescribing operation of the embedding module 128.

In Algorithm 2, line 1 corresponds to functionality performed by thegraph time-series module 124. Lines 2-4 describe functionality performedby the temporal modeling module 126, and line 5 is representative of theembedding module 128 generating the time-series of network embeddings222. Lines 6 and 7 are representative functionality optionally performedby the T-SS module 130 in generating the network embeddings 110.

Algorithm 2 Input: one of the τ-graph time-series representation or theϵ-graph time-series representation and a base embedding method f (e.g.,GraphWave, role2vec) 1:  Construct a graph time-series G = {G₁, G₂, ...,G_(t)} using a graph time-series representation output by the graphtime-series module 2:  Initialize Z₀ to all zeroes 3:  for each G_(t) ∈G do:   

 for t = 1, 2, ..., 4:   Use Algorithm 1 to derive the temporalreachability graph for G_(t) 5:   Compute node embedding matrix Z_(t)using the base embedding method f with the temporal reachability graphderived from Algorithm 1. 6:   Concatenate or aggregate (using sum,mean, etc.) the embedding matrix (e.g., Z _(t) = (1 − θ)Z _(t-1) +θZ_(t), where Z _(t) represents the temporally weighted embedding usingthe above exponential weighting kernel

 (·) and 0 ≤ θ ≤ 1 is a hyperparameter that controls the importance ofpast information relative to more recent information. 7: return Z _(t)(temporally weighted embeddings using

 and θ) or Z = [Z₁ Z₂ ...Z_(t)] (concatenated embeddings).

As noted above, the time-series of network embeddings 222 generated bythe embedding module 128 are representative of an instance of thenetwork embeddings 110 output by the network representation system 104.In some implementations, the time-series of network embeddings 222 arefurther processed by the T-SS module 222 using one or more temporalfusion techniques for output as the network embeddings 110. Forinstance, in some implementations the T-SS module 130 generatesconcatenated network embeddings 224 from the time-series of networkembeddings 222. To do so, given the time-series of network embeddings222, represented as {Z_(t)}_(t=1) ^(T), the T-SS module 130 concatenatesthe network embeddings as Z=[Z₁ . . . Z_(T)]. In some implementations,the T-SS module 130 further weights the time-series of networkembeddings 222 based on time. Alternatively or additionally, the T-SSmodule 130 is configured to moderate the influence of the time-series ofnetwork embeddings 222 by devoting a larger embedding size to morerecent embeddings and/or obtaining a low-rank approximation ofembeddings that occur further in the past.

In doing so, the T-SS module 130 effectively compresses embeddings inthe time-series of network embeddings 222 that occur further in thepast, which preserves an integrity of the resulting network embeddings110 because recent embeddings are of greater importance than previousembeddings when used to generate prediction 112. Additionally,compressing embeddings that occurred further in the past allows for alarger embedding dimension, thus biasing the embeddings toward morerecent events occurring in network data 108 to prepare the networkembeddings 110 for temporal prediction tasks. Alternatively, the T-SSmodule 130 is configured to generate aggregated network embeddings 226by aggregating the time-series of network embeddings 222, such that theaggregated network embeddings 226 represent a sum, a mean, and so forthof the time-series of network embeddings 222. An example manner in whichthe T-SS module 130 generates the concatenated network embeddings 224 orthe aggregated network embeddings 226 is set forth above in lines 6 and7 of Algorithm 2.

The time-series of network embeddings 222, the concatenated networkembeddings 224, or the aggregated network embeddings 226 are then outputby the network representation system 104 as network embeddings 110 forthe network data 108. Because the network embeddings 110 comprise alow-dimensional latent space representation of the network data 108, thenetwork embeddings 110 are useable by one or more prediction modelsconfigured to output a prediction pertaining to the network data 108,such as one or more attributes for a node 116 or a future edge 118between two or more nodes 116. Having considered example details ofgenerating network embeddings for network data, consider now an examplesystem to generate predictions for the network data using the networkembeddings.

FIG. 5 illustrates an example system 500 useable to generate one or morepredictions 112 regarding network data 108, when provided as input withnetwork embeddings 110 derived from the network data 108 according tothe techniques described herein. In the illustrated example, system 500includes the prediction module 132 of the prediction system 106. System500 is configured to be implemented on a single computing device (e.g.,computing device 102 of FIG. 1 ) or a combination of multiple computingdevices, as described in further detail below with respect to FIG. 8 .

The prediction module 132 is configured to implement a prediction modelthat has been trained to perform a particular task or objective (e.g.,link prediction, node attribute prediction, and the like). Given one ofthe time-series of network embeddings 222, the concatenated networkembeddings 224, or the aggregated network embeddings 226 output by thenetwork representation system 104 as network embeddings 110, theprediction module 132 is configured to cause the prediction model togenerate prediction 112 by providing the network embeddings 110 as inputto the prediction model. Example predictions 112 output by theprediction system 106 include a transmission path 120 prediction and anode attribute 122 prediction.

While transmission path 120 predictions and a node attribute 122predictions are described herein for exemplary purposes, the prediction112 type output by prediction system 106 is not so limited to theseexample predictions. Rather, the specific type of prediction 112generated by prediction system 106 is dependent on a specific predictionmodel implemented by the prediction module 132, and the predictionmodule 132 is configured to implement any suitable type of predictionmodel that is configured to output a prediction when provided networkembeddings (e.g., embeddings mapping nodes and/or edges of network datato a low-dimensional latent space).

For instance, to generate the transmission path 120 prediction, theprediction module 132 is configured to implement a link prediction modelthat outputs predictions of future edges 118 between nodes 116 whenprovided the network embeddings 110 as input. Alternatively, to generatethe node attribute 122 prediction, the prediction module 132 isconfigured to implement an entity attribute prediction model thatoutputs predictions of at least one attribute value for one or more ofthe nodes 116 when provided the network embeddings 110 as input.

In this manner, the prediction system 106 is configured to implement thenetwork embeddings 110 generated by the network representation system104 to output predictions that indicate at least one of a missingattribute value not included in the network data 108 or a future edge118 between nodes 116 of the network. Accordingly, system 500 isconfigured to generate a prediction by leveraging network data 108obtained from a particular network data source 134 (e.g., a socialnetworking platform, a mobile service provider, a web server, etc.) orfrom a plurality of different network data sources 134, collectivelyrepresented as network 136.

Having considered example systems and techniques for generating networkembeddings 110 that represent network data 108 and using the networkembeddings 110 to generate one or more predictions 112 pertaining to thenetwork data, consider now example procedures to illustrate aspects ofthe techniques described herein.

Example Procedures

The following discussion describes techniques that may be implementedutilizing the previously described systems and devices. Aspects of eachof the procedures may be implemented in hardware, firmware, software, ora combination thereof. The procedures are shown as a set of blocks thatspecify operations performed by one or more devices and are notnecessarily limited to the orders shown for performing the operations bythe respective blocks. In portions of the following discussion,reference may be made to FIGS. 1-5 .

FIG. 6 depicts a procedure 600 in an example implementation of derivingnetwork embeddings that map network data to a low-dimensional latentspace and generating a prediction from the network embeddings using thetechniques described herein. Network data including a plurality of nodesthat each represent an entity in a network and a plurality of edges thateach represent a connection between two of the plurality of nodes andeach include a timestamp indicating a time at which the edge occurred isreceived (block 602). The graph time-series module 124 of the networkrepresentation system 104, for instance, receives at least one timesegment 114 of network data 108, with the time segment 114 including aplurality of nodes 116 and at least one edge 118 that represents aconnection between two of the nodes 116. The network data 108 isreceived from one or more network data sources 134, such as a socialnetworking platform, a mobile service provider, an educational orworkplace entity, a web server, combinations thereof, and so forth.

A determination is made as to whether a graph time-series representationof the network data is to be constrained by a subset number of theplurality of edges included in the network data (block 604). The graphtime-series module 124, for instance, displays a visual prompt at adisplay of a computing device implementing the network representationsystem 104 requesting user input specifying whether graph time-seriesrepresentations 202 of the network data 108 is to be constrained byedges or time included in the individual graph time-seriesrepresentations 202. Alternatively, the graph time-series module 124 isconfigured to automatically, independent of user input, determinewhether the graph time-series representation of network data is to beconstrained by a number of the plurality of edges 118 included inindividual ones of the graph time-series representations 202. In someimplementations, the graph time-series module 124 is configured todefault to constraining individual graph time-series representations 202to include a designated subset number of the plurality of edges 118unless instructed otherwise.

Responsive to determining that the graph time-series representation ofthe network data is not to be constrained by a subset number of theplurality of edges, a τ-graph time-series representation of the networkdata is generated (block 606). The graph time-series module 124, forinstance, generates the τ-graph time-series representation 204 asrepresenting all or a portion of the time segment 114 of the networkdata 108. The τ-graph time-series representation 204 includes a subsetof the nodes 116 that are connected by a subset of the edges 118 havingassociated timestamps that fall within a duration of time encompassed bythe τ-graph time-series representation 204. In implementations where theτ-graph time-series representation 204 does not encompass an entirety ofthe time segment 114, the graph time-series module 124 is configured togenerate a plurality of τ-graph time-series representations 204, eachencompassing a same duration of the time segment 114, such as τ-graphtime-series representations 310, 312, 314, and 316.

Alternatively, responsive to determining that the graph time-seriesrepresentation of the network data is to be constrained by a subsetnumber of the plurality of edges, an ε-graph time-series representationof the network data is generated (block 608). The graph time-seriesmodule 124, for instance, generates the ε-graph time-seriesrepresentation 206 as representing a portion of the plurality of edges118 included in the time segment 114 of the network data 108. Theε-graph time-series representation 206 includes a specified subsetnumber of the plurality of edges 118, such that each ε-graph time-seriesrepresentation 206 generated for the network data 108 includes a samenumber of edges, as well as the nodes 116 connected by those edges. Byconstraining each ε-graph time-series representation 206 based on anamount of included edges 118 rather than time, different ε-graphtime-series representations 206 generated from the network data 108 areconfigured to encompass different durations of time. The ε-graphtime-series representation 206 generated by the graph time-series module124 is represented by one or the ε-graph time-series representations326, 328, and 330.

A temporal graph that provides a structural representation of thenetwork data and incorporates temporal information included in the graphtime-series representation of the network data is generated (block 610).The temporal modeling module 126, for instance, generates a temporalgraph 214 representation of the network data 108 that incorporatestemporal information described by the graph time-series representation202. The particular structure of the temporal graph 214 generated by thetemporal modeling module 126 depends on a particular model employed bythe temporal modeling module 126 in generating the temporal graph 214.For instance, when a snapshot graph model 208 is employed, the temporalgraph 214 is output as a snapshot graph 216. In another example, when atemporal summary graph model 210 is employed, the temporal graph 214 isoutput as a temporal summary graph 218. In yet another example, when atemporal reachability graph model 212 is employed, the temporal graph214 is configured as a temporal reachability graph 220.

In some implementations, the temporal graph 214 is generated to includeweights reflecting a temporal occurrence of edges 118 represented in thetemporal graph 214. For the instance, the temporal modeling module 126is configured to assign weights to edges represented in the temporalgraph 214 according to a timestamp associated with each edge (e.g.,assigning greater weights to more recent edges to emphasize recent nodeconnections in the temporal graph 214). In this manner, the temporalmodeling module 126 is configured to generate weighted versions of thetemporal summary graph 218 and temporal reachability graph 220 instancesof the temporal graph 214.

A time-series of network embeddings that provides a latent spacerepresentation of the plurality of nodes and the plurality of edges inthe network data is derived using the temporal model (block 612). Theembedding module 128 is configured to employ an embedding method giventhe temporal graph 214 as input and generate a time-series of networkembeddings 222 derived from the temporal graph 214. The time-series ofnetwork embeddings 222 captures temporal dependencies representedbetween nodes 116, as indicated by connecting edges 118, of the networkdata 108 as well as temporal structural properties of the network data108 (e.g., amounts and attributes of nodes 116 and amounts of edges118). The particular embedding method implemented by the embeddingmodule 128 is dependent on a particular predictive task or objective forwhich the time-series of network embeddings 222 are to be employed. Thetime-series of network embeddings 222 generated by the embedding module128 are representative of an instance of the network embeddings 110output by the network representation system 104.

In some implementations, the time-series of network embeddings 222 arefurther processed by the T-SS module 222 using one or more temporalfusion techniques for output as the network embeddings 110. Forinstance, in some implementations the T-SS module 130 generatesconcatenated network embeddings 224 from the time-series of networkembeddings 222. In some implementations, the T-SS module 130 furtherweights the time-series of network embeddings 222 based on time.Alternatively or additionally, the T-SS module 130 is configured tomoderate the influence of the time-series of network embeddings 222 bydevoting a larger embedding size to more recent embeddings and/orobtaining a low-rank approximation of embeddings that occur further inthe past. Alternatively, the T-SS module 130 is configured to generateaggregated network embeddings 226 by aggregating the time-series ofnetwork embeddings 222, such that the aggregated network embeddings 226represent a sum, a mean, and so forth of the time-series of networkembeddings 222. The time-series of network embeddings 222, theconcatenated network embeddings 224, or the aggregated networkembeddings 226 are then output by the network representation system 104as network embeddings 110 for the network data 108.

Procedure 600 optionally returns to block 602, as indicated by thedashed arrow returning to block 602 from 612. For instance, in anexample scenario where the network data 108 is received as a continuousstream, operation returns to block 602 for generating a graphtime-series representation, generating a temporal graph, and derivingnetwork embeddings for a subsequent time segment 114 of the network data108. Procedure 600 is configured to repeat the operations set forth inblocks 602-612 until network embeddings have been derived for anentirety of the network data 108.

A prediction that specifies at least one of a future edge in the networkor a node attribute not included in the network data is generated byapplying a prediction model to the time-series of network embeddings(block 614). Given one of the time-series of network embeddings 222, theconcatenated network embeddings 224, or the aggregated networkembeddings 226 output by the network representation system 104 asnetwork embeddings 110, the prediction module 132 is configured to causethe prediction model to generate prediction 112 by providing the networkembeddings 110 as input to the prediction model. Example predictions 112output by the prediction system 106 include a transmission path 120prediction and a node attribute 122 prediction.

While transmission path 120 predictions and a node attribute 122predictions are described herein for exemplary purposes, the prediction112 type output by prediction system 106 is not so limited to theseexample predictions. Rather, the specific type of prediction 112generated by prediction system 106 is dependent on a specific predictionmodel implemented by the prediction module 132, and the predictionmodule 132 is configured to implement any suitable type of predictionmodel that is configured to output a prediction when provided networkembeddings (e.g., embeddings mapping nodes and/or edges of network datato a low-dimensional latent space).

For instance, to generate the transmission path 120 prediction, theprediction module 132 is configured to implement a link prediction modelthat outputs predictions of future edges 118 between nodes 116 whenprovided the network embeddings 110 as input. Alternatively, to generatethe node attribute 122 prediction, the prediction module 132 isconfigured to implement an entity attribute prediction model thatoutputs predictions of at least one attribute value for one or more ofthe nodes 116 when provided the network embeddings 110 as input.

FIG. 7 depicts a procedure 700 in an example implementation ofgenerating a temporal reachability graph that models network data whilepreserving temporal information associated with the network data. Agraph time-series representation of network data that includesinformation describing a plurality of nodes representing differentnetwork entities, a plurality of edges that each specify a connectionbetween two of the plurality of nodes, and a timestamp associated witheach of the plurality of edges is received (block 702). The temporalmodeling module 126, for instance, receives the graph time-seriesrepresentation 202 of at least a portion of a time segment 114 ofnetwork data 108.

A pair of nodes that are not directly connected to one another by one ofthe plurality of edges included in the graph time-series representationis identified (block 704). The temporal modeling module 126, forinstance, provides the graph time-series representation 202 as input toTRG model 212. A determination is made as to whether the pair of nodesare temporally connected (block 706). The TRG model 212 analyzes thegraph time-series representation 202 to determine whether a temporalwalk exists between the node pair. Responsive to determining that thenode pair is not temporally connected, a different pair of nodes isselected (block 708) and operation returns to block 704.

Alternatively, in response to determining that a temporal walk existsbetween the node pair, an edge that directly connects the pair of nodesis generated (block 710). The TRG model 212 is configured to identifythat a pair of nodes are temporally connected responsive to determiningthat a sequence of temporally constrained edges 118 connect the nodepair during a specified time interval. For instance, responsive todetermining that nodes 404 and 408 are temporally connected to oneanother via the sequence of edges 414 and 416, the TRG model 212 addsedge 424 that directly connects nodes 404 and 408. Similarly, responsiveto determining that nodes 404 and 410 are temporally connected via thesequence of edges 414 and 420, the TRG model 212 adds edge 426 thatdirectly connects nodes 404 and 410.

Operation then optionally moves to block 708, as indicated by the dashedarrow from block 710 to block 708. In this manner, the operations setforth in blocks 704-710 are configured to be repeated until all nodepairs of the graph time-series representation 202 have been analyzed todetermine whether an edge should be added to note their temporalconnection. A graphical representation that includes the generatededge(s) as well as the plurality of nodes, the plurality of edges, andthe plurality of timestamps included in the graph time-seriesrepresentation is generated (block 712). The temporal modeling module126, for instance, generates the temporal reachability graph 422 from agraph time-series representation 202 derived from temporal graph 402.The graphical representation is then output as a temporal reachabilitygraph for the network data (block 714). The temporal modeling module126, for instance, outputs the TRG 220 to embedding module 128 for usein deriving node embeddings 110 for the network data 108.

Having described example procedures in accordance with one or moreimplementations, consider now an example system and device that can beutilized to implement the various techniques described herein.

Example System and Device

FIG. 8 illustrates an example system generally at 800 that includes anexample computing device 802 that is representative of one or morecomputing systems and/or devices that may implement the varioustechniques described herein. This is illustrated through inclusion ofthe network representation system 104 and the prediction system 106. Thecomputing device 802 may be, for example, a server of a serviceprovider, a device associated with a client (e.g., a client device), anon-chip system, and/or any other suitable computing device or computingsystem.

The example computing device 802 as illustrated includes a processingsystem 804, one or more computer-readable media 806, and one or more I/Ointerface 808 that are communicatively coupled, one to another. Althoughnot shown, the computing device 802 may further include a system bus orother data and command transfer system that couples the variouscomponents, one to another. A system bus can include any one orcombination of different bus structures, such as a memory bus or memorycontroller, a peripheral bus, a universal serial bus, and/or a processoror local bus that utilizes any of a variety of bus architectures. Avariety of other examples are also contemplated, such as control anddata lines.

The processing system 804 is representative of functionality to performone or more operations using hardware. Accordingly, the processingsystem 804 is illustrated as including hardware elements 810 that may beconfigured as processors, functional blocks, and so forth. This mayinclude implementation in hardware as an application specific integratedcircuit or other logic device formed using one or more semiconductors.The hardware elements 810 are not limited by the materials from whichthey are formed or the processing mechanisms employed therein. Forexample, processors may be comprised of semiconductor(s) and/ortransistors (e.g., electronic integrated circuits (ICs)). In such acontext, processor-executable instructions may beelectronically-executable instructions.

The computer-readable storage media 806 is illustrated as includingmemory/storage 812. The memory/storage 812 represents memory/storagecapacity associated with one or more computer-readable media. Thememory/storage component 812 may include volatile media (such as randomaccess memory (RAM)) and/or nonvolatile media (such as read only memory(ROM), Flash memory, optical disks, magnetic disks, and so forth). Thememory/storage component 812 may include fixed media (e.g., RAM, ROM, afixed hard drive, and so on) as well as removable media (e.g., Flashmemory, a removable hard drive, an optical disc, and so forth). Thecomputer-readable media 806 may be configured in a variety of other waysas further described below.

Input/output interface(s) 808 are representative of functionality toallow a user to enter commands and information to computing device 802,and also allow information to be presented to the user and/or othercomponents or devices using various input/output devices. Examples ofinput devices include a keyboard, a cursor control device (e.g., amouse), a microphone, a scanner, touch functionality (e.g., capacitiveor other sensors that are configured to detect physical touch), a camera(e.g., which may employ visible or non-visible wavelengths such asinfrared frequencies to recognize movement as gestures that do notinvolve touch), and so forth. Examples of output devices include adisplay device (e.g., a monitor or projector), speakers, a printer, anetwork card, tactile-response device, and so forth. Thus, the computingdevice 802 may be configured in a variety of ways as further describedbelow to support user interaction.

Various techniques may be described herein in the general context ofsoftware, hardware elements, or program modules. Generally, such modulesinclude routines, programs, objects, elements, components, datastructures, and so forth that perform particular tasks or implementparticular abstract data types. The terms “module,” “functionality,” and“component” as used herein generally represent software, firmware,hardware, or a combination thereof. The features of the techniquesdescribed herein are platform-independent, meaning that the techniquesmay be implemented on a variety of commercial computing platforms havinga variety of processors.

An implementation of the described modules and techniques may be storedon or transmitted across some form of computer-readable media. Thecomputer-readable media may include a variety of media that may beaccessed by the computing device 802. By way of example, and notlimitation, computer-readable media may include “computer-readablestorage media” and “computer-readable signal media.”

“Computer-readable storage media” may refer to media and/or devices thatenable persistent and/or non-transitory storage of information incontrast to mere signal transmission, carrier waves, or signals per se.Thus, computer-readable storage media refers to non-signal bearingmedia. The computer-readable storage media includes hardware such asvolatile and non-volatile, removable and non-removable media and/orstorage devices implemented in a method or technology suitable forstorage of information such as computer readable instructions, datastructures, program modules, logic elements/circuits, or other data.Examples of computer-readable storage media may include, but are notlimited to, RAM, ROM, EEPROM, flash memory or other memory technology,CD-ROM, digital versatile disks (DVD) or other optical storage, harddisks, magnetic cassettes, magnetic tape, magnetic disk storage or othermagnetic storage devices, or other storage device, tangible media, orarticle of manufacture suitable to store the desired information andwhich may be accessed by a computer.

“Computer-readable signal media” may refer to a signal-bearing mediumthat is configured to transmit instructions to the hardware of thecomputing device 802, such as via a network. Signal media typically mayembody computer readable instructions, data structures, program modules,or other data in a modulated data signal, such as carrier waves, datasignals, or other transport mechanism. Signal media also include anyinformation delivery media. The term “modulated data signal” means asignal that has one or more of its characteristics set or changed insuch a manner as to encode information in the signal. By way of example,and not limitation, communication media include wired media such as awired network or direct-wired connection, and wireless media such asacoustic, RF, infrared, and other wireless media.

As previously described, hardware elements 810 and computer-readablemedia 806 are representative of modules, programmable device logicand/or fixed device logic implemented in a hardware form that may beemployed in some embodiments to implement at least some aspects of thetechniques described herein, such as to perform one or moreinstructions. Hardware may include components of an integrated circuitor on-chip system, an application-specific integrated circuit (ASIC), afield-programmable gate array (FPGA), a complex programmable logicdevice (CPLD), and other implementations in silicon or other hardware.In this context, hardware may operate as a processing device thatperforms program tasks defined by instructions and/or logic embodied bythe hardware as well as a hardware utilized to store instructions forexecution, e.g., the computer-readable storage media describedpreviously.

Combinations of the foregoing may also be employed to implement varioustechniques described herein. Accordingly, software, hardware, orexecutable modules may be implemented as one or more instructions and/orlogic embodied on some form of computer-readable storage media and/or byone or more hardware elements 810. The computing device 802 may beconfigured to implement particular instructions and/or functionscorresponding to the software and/or hardware modules. Accordingly,implementation of a module that is executable by the computing device802 as software may be achieved at least partially in hardware, e.g.,through use of computer-readable storage media and/or hardware elements810 of the processing system 804. The instructions and/or functions maybe executable/operable by one or more articles of manufacture (forexample, one or more computing devices 802 and/or processing systems804) to implement techniques, modules, and examples described herein.

The techniques described herein may be supported by variousconfigurations of the computing device 802 and are not limited to thespecific examples of the techniques described herein. This functionalitymay also be implemented all or in part through use of a distributedsystem, such as over a “cloud” 814 via a platform 816 as describedbelow.

The cloud 814 includes and/or is representative of a platform 816 forresources 818. The platform 816 abstracts underlying functionality ofhardware (e.g., servers) and software resources of the cloud 814. Theresources 818 may include applications and/or data that can be utilizedwhile computer processing is executed on servers that are remote fromthe computing device 802. Resources 818 can also include servicesprovided over the Internet and/or through a subscriber network, such asa cellular or Wi-Fi network.

The platform 816 may abstract resources and functions to connect thecomputing device 802 with other computing devices. The platform 816 mayalso serve to abstract scaling of resources to provide a correspondinglevel of scale to encountered demand for the resources 818 that areimplemented via the platform 816. Accordingly, in an interconnecteddevice embodiment, implementation of functionality described herein maybe distributed throughout the system 800. For example, the functionalitymay be implemented in part on the computing device 802 as well as viathe platform 816 that abstracts the functionality of the cloud 814.

CONCLUSION

Although the invention has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the invention defined in the appended claims is not necessarilylimited to the specific features or acts described. Rather, the specificfeatures and acts are disclosed as example forms of implementing theclaimed invention.

What is claimed is:
 1. In a digital medium environment for derivingnetwork embeddings that provide a latent representation of nodes andedges in network data for a network, a method implemented by at leastone computing device, the method comprising: receiving, by the at leastone computing device, network data describing a plurality of entitiesand a plurality of connections that each connect a pair of the pluralityof entities; generating, by the at least one computing device, aplurality of graph time-series representations from the network data toeach encompass a same number of the plurality of connections included inthe network data, each of the plurality of graph time-seriesrepresentations comprising a subset of the plurality of entities and asubset of the plurality of connections included in the network data;generating, by the at least one computing device, a temporal graph ofthe network data based on the plurality of graph time-seriesrepresentations, the temporal graph comprising a graph structurerepresentation of the network data that incorporates temporalinformation described by the plurality of graph time-seriesrepresentations; and deriving, by the at least one computing device, atime-series of network embeddings for the network data from the temporalgraph, the time-series of network embeddings comprising a latentrepresentation of the plurality of entities in the network data.
 2. Themethod as recited in claim 1, wherein each of the plurality of entitiesrepresents one of a computing device, a physical location, a userprofile, an Internet Protocol (IP) address, a Uniform ResourceIdentifier (URI) for a resource accessible via the network, a userprofile, or an institution identifying a plurality of user profiles, andeach of the plurality of entities is associated with one or moreattribute values that describe characteristics of the entity.
 3. Themethod as recited in claim 1, wherein each of the plurality ofconnections represents one of a transfer of data between the pair of theplurality of entities connected by the connection or a satisfaction of athreshold physical proximity between the pair of the plurality ofentities connected by the connection.
 4. The method as recited in claim1, wherein each of the plurality of graph time-series representationsare generated to encompass a fixed duration of time.
 5. The method asrecited in claim 1, wherein a first one of the plurality of graphtime-series representations is generated to encompass a first period oftime and a second one of the plurality of graph time-seriesrepresentations is generated to encompass a second period of time, thefirst period of time encompassing a duration that is greater than orless than a duration encompassed by the second period of time.
 6. Themethod as recited in claim 1, wherein receiving the network datacomprises receiving the network data as a continuous stream of networkdata that describes real-time changes to the plurality of entities andthe plurality of connections and each of the plurality of graphtime-series representations represent an interval of the continuousstream of network data, the interval comprising one of a fixed durationor a fixed number of connections.
 7. The method as recited in claim 1,wherein the temporal graph comprises a temporal summary graph thatweights individual ones of the plurality of connections based on atimestamp associated with the connection.
 8. The method as recited inclaim 1, wherein the temporal graph comprises a temporal reachabilitygraph that adds at least one connection between two of the plurality ofentities that are not directly connected via one of the plurality ofconnections included in the network data.
 9. The method as recited inclaim 8, further comprising identifying, by the at least one computingdevice, the at least one connection between the two of the plurality ofentities that are not directly connected via one of the plurality ofconnections included in the network data responsive to identifying thata sequence of the plurality of connections in the network data connectthe two of the plurality of entities during a time-constrained interval.10. The method as recited in claim 1, further comprising generating, bythe at least one computing device, a prediction from the time-series ofnetwork embeddings, the prediction comprising an attribute value for oneof the plurality of entities, wherein the attribute value is notincluded in the network data.
 11. The method as recited in claim 1,further comprising generating, by the at least one computing device, aprediction from the time-series of network embeddings, the predictioncomprising a transmission path that specifies at least one futureconnection between at least two of the plurality of entities included inthe network data, wherein the at least one future connection is notincluded in the network data.
 12. The method as recited in claim 1,wherein each of the plurality of graph time-series representationsencompasses a different interval of the network data, the method furthercomprising: p1 performing, by the at least one computing device, thegenerating the temporal graph of the network data and the deriving thetime-series of network embeddings for each of the plurality of graphtime-series representations; concatenating or aggregating, by the atleast one computing device, the derived plurality of time-series ofnetwork embeddings; and generating, by the at least one computingdevice, a prediction based on the concatenated or aggregated networkembeddings.
 13. In a digital medium environment for generating atemporal graph of network data that adds temporally constrainedconnections between nodes not directly connected in the network data, amethod implemented by at least one computing device, the methodcomprising: receiving, by the at least one computing device, a graphtime-series representation of network data, the graph time-seriesrepresentation including information describing a plurality of nodesrepresenting different entities in a network, one or more edges thateach specify a connection between two of the plurality of nodes, and atimestamp associated with each of the one or more edges; generating, bythe at least one computing device, a temporal reachability graph of thenetwork data by: identifying a pair of nodes of the plurality of nodesthat are not directly connected to one another by one of the one or moreedges included in the graph time-series representation; determiningwhether the pair of nodes are temporally connected; and responsive todetermining that the pair of nodes are temporally connected, generatingan edge that directly connects the pair of nodes; and outputting, by theat least one computing device, the temporal reachability graph as agraphical representation of the network data that includes the pluralityof nodes, the one or more edges, and the one or more timestamps includedin the graph time-series representation and the edge that directlyconnects the pair of nodes not directly connected in the graphtime-series representation.
 14. The method as recited in claim 13,wherein the plurality of nodes represent a plurality of computingdevices and each of the one or more edges represents a transmission ofdata from one of the plurality of computing devices to another one ofthe plurality of computing devices at a time indicated by acorresponding timestamp.
 15. The method as recited in claim 13, whereinthe plurality of nodes represent a plurality of computing devices andthe one or more edges each indicate that one of the plurality ofcomputing devices was within a threshold physical distance to anotherone of the plurality of computing devices at a time indicated by acorresponding timestamp.
 16. The method as recited in claim 13, whereindetermining that the pair of nodes are temporally connected comprisesidentifying that a sequence of at least two of the one or more edgesincluded in the graph time-series representation connecting the pair ofnodes are associated with timestamps that occur during a thresholdduration.
 17. The method as recited in claim 13, further comprisinggenerating, by the at least one computing device, a weighted temporalreachability graph from the temporal reachability graph by assigning amathematical weight to each of the one or more edges included in thetemporal reachability graph based on an amount of time required tocomplete each edge and a number of edges in the temporal reachabilitygraph that connect the two of the plurality of nodes connected by theedge being weighted.
 18. The method as recited in claim 13, furthercomprising: deriving, by the at least one computing device, atime-series of network embeddings from the temporal reachability graphthat provides a latent representation of node attributes for theplurality of nodes and a latent representation of edge attributes forthe plurality of edges; and generating, by the at least one computingdevice, a prediction from the time-series of network embeddings.
 19. Ina digital medium environment for deriving network embeddings thatprovide a latent representation of nodes and edges in network data for anetwork, a system comprising: one or more processors; and at least onecomputer-readable storage medium having instructions stored thereon thatare executable by the one or more processors to perform operationscomprising: receiving network data describing a plurality of nodes thateach represent an entity in a network, a plurality of connections thateach represent a connection between a pair of the plurality of nodes,and a plurality of timestamps that each identify a time at which acorresponding one of the plurality of connections occurred; generating aplurality of graph time-series representations from the network data,each of the plurality of graph time-series representations comprising asame number subset of the plurality of connections; generating, for eachof the plurality of graph time-series representations, a temporalreachability graph of the network data by: identifying a pair of nodesin the graph time-series representation that are not directly connectedby one of the same number subset of the plurality of connections;generating an edge that directly connects the pair of nodes responsiveto determining that the pair of nodes are temporally connected by asequence of at least two of the subset of the plurality of connections;and outputting the temporal reachability graph as a graphicalrepresentation of the network data that includes the plurality of nodes,one or more edges, and the one or more timestamps included in the graphtime-series representation and the edge that directly connects the pairof nodes not directly connected in the graph time- seriesrepresentation; and deriving a time-series of network embeddings for thenetwork data from the plurality of temporal reachability graphs, thetime-series of network embeddings comprising a latent representation ofthe plurality of nodes and the one or more of edges in the network data.20. The system as recited in claim 19, the operations further comprisinggenerating a weighted temporal reachability graph from the temporalreachability graph by assigning a mathematical weight to each of the oneor more edges based on an amount of time required to complete each edgeand a number of edges in the temporal reachability graph that connecttwo nodes connected by the edge being weighted.